Theoretical viscoelastic functions, reduced

Theoretical Viscoelastic Functions Reduced in Dimensionless Form... 

It has been remarked that time (frequency) - temperature reduced data on carbon black filled rubbers exhibit increased scatter compared to similar data on unfilled polymers. Payne (102) ascribes this to the effects of secondary aggregation. Possibly related to this are the recent observations of Adicoff and Lepie (174) who show that the WLF shift factors of filled rubbers giving the best fit are slightly different for the storage and loss moduli and that they are dependent on strain. Use of different shift factors for the various viscoelastic functions is not justified theoretically and choice of a single, mean ar-funetion is preferred as an approximation. The result, of course, is increased scatter of the experimental points of the master curve. This effect is small for carbon black... 

To show the effect of diluent o.n the detailed shapes of viscoelastic functions, it is convenient to employ corresponding-state plots as in Section C of Chapter 12. For the relaxation spectrum, we plot log H - log Tc/Mq against log t - log a o/kT). Of course, for a single polymer and its solutions the only variables are fo and c (which in the pure polymer becomes p). In Fig. 17-9, poly(vinyl acetate) is compared in this manner with its 50% solution in tri-m-cresyl phosphate. The values of log fo at 40°C for these two systems are 1.75 and -5.25, respectively—the diluent reduces the local friction coefficient by a factor of 10. The curves after reduction coincide at the bottom of the transition zone because this is fixed by the corresponding-state conditions, and are rather similar in shape throughout. However, the diluent causes the spectrum to rise somewhat more sharply from the theoretical slope of -5 at short times but at still shorter times it crosses the spectrum of the pure polymer, and its entrance into the glassy zone involves a broader maximum than the latter. 

The differences in spectral shape are of course reflected in the other viscoelastic functions, especially the loss tangent, which is always the most sensitive. The loss tangents for poly(/t-butyl methacrylate) and three of its solutions are plotted in Fig. 17-11 with the frequency scale reduced in the same way as the abscissa in Fig. 17-10. They show some degree of broadening with increasing dilution, but their maxima remain considerably above the theoretical value of 1.0 which would be predicted throughout the rq ition zone by the flexible chain theory in its simple form. Similar behavior has bwn reported for concentrated solutions of polystyrene in tricresyl phosphate, by Wasser and Kurath. ... 

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